# GMTMATH

NAME
SYNOPSIS
DESCRIPTION
OPTIONS
ASCII FORMAT PRECISION
BEWARE
EXAMPLES
BEWARE
REFERENCES

## NAME

 gmtmath − Reverse Polish Notation calculator for data tables

## SYNOPSIS

 gmtmath [ −At_f(t).d ] [ −Ccols ] [ −Fcols ] [ −H[i][nrec] ] [ −I ] [ −M[i|o][flag] ] [ −Nn_col/t_col ] [ −Q ] [ −S[f|l] ] [ −Tt_min/t_max/t_inc|tfile ] [ −V ] [ −b[i|o][s|S|d|D][ncol] ] [ −f[i|o]colinfo ] operand [ operand ] OPERATOR [ operand ] OPERATOR ... = [ outfile ]

## DESCRIPTION

 gmtmath will perform operations like add, subtract, multiply, and divide on one or more table data files or constants using Reverse Polish Notation (RPN) syntax (e.g., Hewlett-Packard calculator-style). Arbitrarily complicated expressions may therefore be evaluated; the final result is written to an output file [or standard output]. When two data tables are on the stack, each element in file A is modified by the corresponding element in file B. However, some operators only require one operand (see below). If no data tables are used in the expression then options −T, −N can be set (and optionally −b to indicate the data domain. If STDIN is given, will be read and placed on the stack as if a file with that content had been given on the command line. By default, all columns except the "time" column are operated on, but this can be changed (see −C).
 operand
 If operand can be opened as a file it will be read as an ASCII (or binary, see −bi) table data file. If not a file, it is interpreted as a numerical constant or a special symbol (see below). The special argument STDIN means that stdin will be read and placed on the stack; STDIN can appear more than once if necessary.
 outfile is a table data file that will hold the final result. If not given then the output is sent to stdout.
 OPERATORS
 Choose among the following operators:
 Operator n_args Returns ABS 1 abs (A). ACOS 1 acos (A). ACOSH 1 acosh (A). ADD 2 A + B. AND 2 NaN if A and B == NaN, B if A == NaN, else A. ASIN 1 asin (A). ASINH 1 asinh (A). ATAN 1 atan (A). ATAN2 2 atan2 (A, B). ATANH 1 atanh (A). BEI 1 bei (A). BER 1 ber (A). CEIL 1 ceil (A) (smallest integer >= A). CHICRIT 2 Critical value for chi-squared-distribution, with alpha = A and n = B. CHIDIST 2 chi-squared-distribution P(chi2,n), with chi2 = A and n = B. CORRCOEFF 2 Correlation coefficient r(A, B). COL 1 Places column A on the stack. COS 1 cos (A) (A in radians). COSD 1 cos (A) (A in degrees). COSH 1 cosh (A). CPOISS 2 Cumulative Poisson distribution F(x,lambda), with x = A and lambda = B. D2DT2 1 d^2(A)/dt^2 2nd derivative. D2R 1 Converts Degrees to Radians. DILOG 1 dilog (A). DIV 2 A / B. DDT 1 d(A)/dt 1st derivative. DUP 1 Places duplicate of A on the stack. ERF 1 Error function erf (A). ERFC 1 Complementary Error function erfc (A). ERFINV 1 Inverse error function of A. EQ 2 1 if A == B, else 0. EXCH 2 Exchanges A and B on the stack. EXP 1 exp (A). FCRIT 3 Critical value for F-distribution, with alpha = A, n1 = B, and n2 = C. FDIST 3 F-distribution Q(F,n1,n2), with F = A, n1 = B, and n2 = C. FLIPUD 1 Reverse order of each column FLOOR 1 floor (A) (greatest integer <= A). FMOD 2 A % B (remainder). GE 2 1 if A >= B, else 0. GT 2 1 if A > B, else 0. HYPOT 2 hypot (A, B) = sqrt (A*A + B*B). I0 1 Modified Bessel function of A (1st kind, order 0). I1 1 Modified Bessel function of A (1st kind, order 1). IN 2 Modified Bessel function of A (1st kind, order B). INT 1 Numerically integrate A. INV 1 1 / A. ISNAN 1 1 if A == NaN, else 0. J0 1 Bessel function of A (1st kind, order 0). J1 1 Bessel function of A (1st kind, order 1). JN 2 Bessel function of A (1st kind, order B). K0 1 Modified Kelvin function of A (2nd kind, order 0). K1 1 Modified Bessel function of A (2nd kind, order 1). KN 2 Modified Bessel function of A (2nd kind, order B). KEI 1 kei (A). KER 1 ker (A). LE 2 1 if A <= B, else 0. LMSSCL 1 LMS scale estimate (LMS STD) of A. LOG 1 log (A) (natural log). LOG10 1 log10 (A) (base 10). LOG1P 1 log (1+A) (accurate for small A). LOG2 1 log2 (A) (base 2). LOWER 1 The lowest (minimum) value of A. LRAND 2 Laplace random noise with mean A and std. deviation B. LSQFIT 1 Let current table be [A | b]; return least squares solution x = A \ b. LT 2 1 if A < B, else 0. MAD 1 Median Absolute Deviation (L1 STD) of A. MAX 2 Maximum of A and B. MEAN 1 Mean value of A. MED 1 Median value of A. MIN 2 Minimum of A and B. MODE 1 Mode value (Least Median of Squares) of A. MUL 2 A * B. NAN 2 NaN if A == B, else A. NEG 1 -A. NEQ 2 1 if A != B, else 0. NRAND 2 Normal, random values with mean A and std. deviation B. OR 2 NaN if A or B == NaN, else A. PLM 3 Associated Legendre polynomial P(-1
 SYMBOLS
 The following symbols have special meaning:
 PI 3.1415926... E 2.7182818... T Table with t-coordinates

## OPTIONS

 −A Requires −N and will partially initialize a table with values from the given file containing t and f(t) only. The t is placed in column t_col while f(t) goes into column n_col - 1 (see −N). −C Select the columns that will be operated on until next occurrence of −C. List columns separated by commas; ranges like 1,3-5,7 are allowed. −C (no arguments) resets the default action of using all columns except time column (see −N). −Ca selects all columns, including time column, while −Cr reverses (toggles) the current choices. −F Give a comma-separated list of desired columns or ranges that should be part of the output (0 is first column) [Default outputs all columns]. −H Input file(s) has Header record(s). Number of header records can be changed by editing your .gmtdefaults4 file. If used, GMT default is 1 header record. Use −Hi if only input data should have header records [Default will write out header records if the input data have them]. −I Reverses the output row sequence from ascending time to descending [ascending]. −M Multiple segment file(s). Segments are separated by a special record. For ASCII files the first character must be flag [Default is ’>’]. For binary files all fields must be NaN and −b must set the number of output columns explicitly. By default the −M setting applies to both input and output. Use −Mi and −Mo to give separate settings. −N Select the number of columns and the column number that contains the "time" variable. Columns are numbered starting at 0 [2/0]. −Q Quick mode for scalar calculation. Shorthand for −Ca −N1/0 −T0/0/1. −S Only report the first or last row of the results [Default is all rows]. This is useful if you have computed a statistic (say the MODE) and only want to report a single number instead of numerous records with identical values. Append l to get the last row and f to get the first row only [Default]. −T Required when no input files are given. Sets the t-coordinates of the first and last point and the equidistant sampling interval for the "time" column (see −N). If there is no time column (only data columns), give −T with no arguments; this also implies −Ca. Alternatively, give the name of a file whose first column contains the desired t-coordinates which may be irregular. −V Selects verbose mode, which will send progress reports to stderr [Default runs "silently"]. −bi Selects binary input. Append s for single precision [Default is d (double)]. Uppercase S (or D) will force byte-swapping. Optionally, append ncol, the number of columns in your binary file if it exceeds the columns needed by the program. −bo Selects binary output. Append s for single precision [Default is d (double)]. Uppercase S (or D) will force byte-swapping. Optionally, append ncol, the number of desired columns in your binary output file. [Default is same as input, but see −F]

## ASCII FORMAT PRECISION

 The ASCII output formats of numerical data are controlled by parameters in your .gmtdefaults4 file. Longitude and latitude are formatted according to OUTPUT_DEGREE_FORMAT, whereas other values are formatted according to D_FORMAT. Be aware that the format in effect can lead to loss of precision in the output, which can lead to various problems downstream. If you find the output is not written with enough precision, consider switching to binary output (−bo if available) or specify more decimals using the D_FORMAT setting.

## BEWARE

 (1) The operator PLM calculates the associated Legendre polynomial of degree L and order M, and its argument is the cosine of the colatitude which must satisfy -1 <= x <= +1. PLM is not normalized. (2) All derivatives are based on central finite differences, with natural boundary conditions.